1. Parallel and Perpendicular Lines
Notecards Unit 3
Parallel and Perpendicular Lines
Distance and Midpoint
Equations for Lines

2. Definition of Parallel Lines (//)
Notecard 49
Definition of Parallel Lines (//)
Two lines that lie in the same plane that never intersect are called parallel.
Lines m & n are
parallel

3. Definition of Skew Lines
Notecard 50
Definition of Skew Lines
Two lines are skew if they do not intersect and do not lie in the same plane.
Lines m & k are skew

4. Definition of Parallel Planes
Notecard 51
Definition of Parallel Planes
Two planes that do not intersect.
Planes T & U are
parallel

5. Definition of Perpendicular Lines
Notecard 52
Definition of Perpendicular Lines
Perpendicular lines are lines that intersect to form a right angle.
Line CD and
Line DE are
perpendicular

6. Definition of Perpendicular Planes
Notecard 53
Definition of Perpendicular Planes
Planes that intersect to form a right angle.
Planes ABC and
ABG are perpendicular.

7. Notecard 54 Parallel Postulate
If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.
There is exactly
one line through
P parallel to line m.

8. Perpendicular Postulate
Notecard 55
Perpendicular Postulate
If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.
There is exactly one line
through P perpendicular
to line m.

9. Transitive Property of Parallel Lines
Notecard 56
Transitive Property of Parallel Lines
If two lines are // to the same line, then they
are // to each other.

10. Slope – the change in y divided by the change in x
Notecard 57
Slope – the change in y divided by the change in x
Formula: Slope = y2 – y1
x2 – x1

11. Postulate – Slope of Parallel Lines
Notecard 58
Postulate – Slope of Parallel Lines
In a coordinate plane, two non-vertical lines are // if and only if they have the same slope.
Any two vertical lines are parallel.

12. Postulate – Slope of Perpendicular Lines
Notecard 59
Postulate – Slope of Perpendicular Lines
In a coordinate plane, two non-vertical lines are perpendicular if and only if the product of their slopes is -1. (They are negative reciprocals.)
Horizontal lines are perpendicular to vertical lines.

13. Definition of Midpoint & Formula
Notecard 60
Definition of Midpoint & Formula
The point that divides a segment into two congruent segments.
Midpoint =

14. Notecard 61
Distance Formula: the ditance between two points (x1, y1) and (x2, y2) d =

15. Definition – Distance from a point to a Line
Notecard 62
Definition – Distance from a point to a Line
The distance between a point and a line must be measured with a  segment from the point to the line.

16. Definition – Distance between 2 Parallel Lines
Notecard 63
Definition – Distance between 2 Parallel Lines
The distance between 2 // lines must be measured with a segment  to both lines.

17. Notecard 64
Theorem
If 2 lines intersect to form a linear pair of congruent angles, then the lines are .
Lines g & h are 

18. Notecard 65
Theorem
If two lines are , then they intersect to form 4 right angles.
Angles 1, 2, 3, & 4 are
all right angles.

19. Notecard 66
Theorem
If two sides of two adjacent acute angles are , then the angles are complementary.
Angles 1 & 2 are
complementary

20. Perpendicular Transversal Theorem
Notecard 67
Perpendicular Transversal Theorem
If a transversal is  to one of two // lines, then it is perpendicular to the other.
If line j  line h and line h
and line k are //, then
line j  line k

21. Lines Perpendicular to a Transversal Theorem
Notecard 68
Lines Perpendicular to a Transversal Theorem
In a plane, if 2 lines are  to the same line, then they are // to each other.
If lines m & n are both  to
line p, then lines m & n are //.